Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20266224 | C2 | semidirect |
| 2. #20266218 | C2 | semidirect |
| 3. #20266102 | C2 | semidirect |
| 4. #20266095 | C2 | semidirect |
| 5. #20266093 | C2 | semidirect |
| 6. #20266068 | C2 | semidirect |
| 18. #15692200 | C4 | semidirect |
| 19. #15692199 | C4 | semidirect |
| 20. #15692196 | C4 | semidirect |
| 22. D16×C101 | C4 | semidirect |
| 34. Dic404 | C2×C4 | semidirect |
| 39. #13108049 | C2×C4 | semidirect |
| 41. D8×C101 | C2×C4 | semidirect |
| 42. C16×C101 | C2×C4 | semidirect |
| 76. C101 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #87938 | semidirect |
| 107. D8 | C2×#87938 | semidirect |
| 118. C16 | C2×#87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266224 | 2 |
| #20266218 | 2 |
| #20266102 | 2 |
| #20266095 | 2 |
| #20266093 | 2 |
| #20266068 | 2 |
| #20265611 | 2 |
| AGL(1,ℤ/16) | 101 |